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Data Analysis Machine Learning and Applications Episode 1 Part 10

Tham khảo tài liệu 'data analysis machine learning and applications episode 1 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 212 Antonello D Ambra Pietro Amenta and Valentin Rousson values a negative value zero and a positive value the sum of the loadings being zero for each component defining hence proper contrasts of categories . The goal of Simple NSCA is to find the optimal system of components among the simple ones where optimality is calculated according to Gervini and Rousson 2004 . The percentage of extracted variability V L accounted by a system L of m min I J 1 components is given by rs g Í k 2 V L S SL k 1 L k 1 SL k 1 1L k 1 S lk where lk is the kth column of L and where L k 1 is the m X k 1 matrix containing the first k 1 columns of L. Whereas the numerator of the first term of this sum is equal to the variance of the first component the numerator of the kth term can be interpreted as the variance of the part of the kth component which is not explained by which is independent from the previous k 1 components. Thus correlations are penalized by this criterion which is hence uniquely maximized by PCA i.e. by taking L Em the matrix of the first m eigenvectors of S Gervini and Rousson 2004 . The optimality of a system L is then calculated as V L V Em . In our sequential algorithms below the kth simple component is obtained by regressing the original row column categories on the previous k 1 simple components already in the system by computing the first eigenvector of the residual variance hence obtained and by shrinking this eigenvector towards the simple difference component which maximizes optimality. Here are two algorithms providing simple components for the rows and the columns. Simple solutions for the rows 1. Let S nD jn let L be an empty matrix and let S S. 2. Let a a1 . aI be the first eigenvector of S. 3. For each cut-off value among g 0 a11 . aI consider the shrunken vector b g b1 g . bl g with elements bk g sign ak if ajt g and bk g 0 otherwise for k 1 . I . Update and normalize it such that 52 bk g 0 and Eb2 g 1 4. Include into the system the difference component b